Sometimes a measurement of dynamic pressure is needed, and, often, the dynamic pressure is small in comparison to the static or quasi-static pressure in the environment where the measurement is needed. For example, it is often of interest to sense underwater acoustic waves at depths where the hydrostatic pressure overwhelms by many orders of magnitude the acoustic waves. The dynamic pressure is here understood to be a changing pressure, such as the pressure change accompanying the passage of an underwater or airborne acoustic wave, but can include variations in pressure that occur much more slowly or much more rapidly.
One way of measuring dynamic pressure is to sense the change in diameter of a compliant mandrel exposed to the dynamic pressure. A cylindrical body, possibly hollow, or in other words air-backed, is often used as a compliant mandrel; using an air-backed, instead of a solid mandrel, results in a more compliant mandrel. The changing pressure ultimately produces a changing circumferential stress, also called hoop stress. At the same time, in what is called Poisson's effect, when an increase in pressure squeezes radially on the mandrel, the mandrel lengthens at the same time it thins, i.e. the mandrel experiences both axial and circumferential strains. In monitoring dynamic pressure, a sensor can base its measurement on either circumferential strain of a mandrel, i.e. a change in diameter of the mandrel, or on axial strain if the mandrel is of a construction that exhibits an appreciable Poisson's effect.
To transform a change in shape of a deformable mandrel into a signal corresponding to the dynamic pressure acting on the mandrel, an optical fiber having one or more Bragg gratings is often affixed to the mandrel so that, depending on how it is affixed, the optical fiber is forced to undergo either the same axial strain or the same hoop strain as the mandrel.
A Bragg grating is created over a length of optical fiber by exposing segments along the length to different light in the ultraviolet range causing different indices of refraction. When light is passed through the optical fiber, the Bragg grating causes an interference pattern that depends on the length over which the Bragg grating extends; when the length changes, the pattern changes, and does so in a way that allows the change in length to be determined. Based on some predetermined correlation, the change in length of the optical fiber is then converted to a change in pressure.
For greater sensitivity, a Bragg grating is positioned at each end of a length of optical fiber affixed to a deformable mandrel. To sense changes in pressure over only a small volume, the optical fiber may be wound, under tension, about the outside of the deformable mandrel. If the pressure increases or decreases, the deformable mandrel changes in diameter, and the length of fiber optic between the Bragg gratings changes; this change in length of the optical fiber between the Bragg gratings at either end of the wound optical fiber can also be sensed by interferometry.
Optical fiber pressure sensors for sensing acoustic pressure in a fluid often must be sensitive to small changes in pressure in an environment of high ambient pressure. These sensors are sometimes constructed by winding an optical fiber, under tension, around a deformable mandrel. Such a construction allows high sensitivity to pressure in a relatively small volume.
Because the pre-strain of an optical fiber winding about a mandrel in such a construction is limited to below a maximum value (determined by fiber reliability and strength), as the ambient pressure increases and so deforms the mandrel more and more, the mandrel is increasingly less likely to deform in response to the small pressures of an acoustic wave, and at some ambient pressure the mandrel will have been squeezed to such an extent that the optical fiber will no longer be in tension. For example, in monitoring underwater acoustic waves, a pressure sensor might be positioned at a depth where, unless the sensor is specially constructed, the hydrostatic pressure would so squeeze the deformable mandrel that the optical fiber would no longer be in tension and so would not shrink in length were the deformable mandrel to further deform in response to an acoustic wave. For a given amount of pre-strain, the pressure at which the fiber becomes slack is a function of the mandrel stiffness. So to measure dynamic pressure in increasingly higher static pressure environments requires an increasingly stiffer, but then less sensitive mandrel. Such a less sensitive mandrel is not always acceptable.
A mandrel for use as part of a pressure sensor will not only deform in response to changes in pressure, but will also deform in response to changes in temperature. In monitoring dynamic pressures, such as acoustic pressures in a fluid, changes in the shape of a mandrel due to changes in temperature are usually of concern only because high temperatures can damage either the mandrel material or the optical fiber, or a large change in length can cause excessive drift in the interferometric signal. However, there are high temperature environments where monitoring dynamic pressure is useful. In some situations where monitoring dynamic pressure is needed, such as deep within an oil well, a pressure sensor is exposed to both high temperatures and high ambient static pressures. Thus, it is important for a pressure sensor to be able to withstand high temperatures and high ambient pressure, and yet still respond to dynamic pressure that is small relative to the ambient pressure.
In many applications it is useful and convenient to monitor dynamic pressure simultaneously at several locations, up to sometimes hundreds of locations. Ideally, in such an application, a single mandrel and optical fiber would be used, with the optical fiber wound about the mandrel only in each location where, with the mandrel deployed in the application, the dynamic pressure is to be sensed. When the optical fiber is wound at more than one location along the length of the mandrel, light of various frequencies can be introduced into the optical fiber and different windings can be made to reflect light of only a particular range of frequencies, depending on the Bragg gratings for the winding. Thus, each winding reflects light of a particular wavelength range back to a diagnostic center where the information from each winding can be extracted from the combined returning signal.
One difficulty in using a single mandrel bearing several optical fiber windings, however, is that the effect of a pressure wave at one location along the mandrel might propagate along the mandrel so as to be sensed at other locations. Another difficulty is that the temperature and ambient pressure a long mandrel experiences can vary significantly along the length of the mandrel. For example, in an oil well application, the down hole span of a mandrel sees a much higher temperature and ambient pressure than the span near the surface. A good design for the down hole span of the multi-sensor is not necessarily a good design for the near surface span; if the mandrel somehow compensates for high ambient pressure down hole, that compensation may not be appropriate for the near-surface span.
Moreover, for a multi-sensor application using a single long mandrel, the mandrel is liable to strain lengthwise because of either its own weight in a vertical deployment, or because of accumulated friction in a deployment where, for example, the mandrel is towed underwater, behind a ship. Such axial strain may stress the optical fiber wound around and laid down along the length of the mandrel, shortening the service life of the optical fiber and also causing excessive drift, over time, in the wavelength of the light reflected by the sensor.
What is needed is a mandrel-wound fiber optic pressure sensor that can measure dynamic pressures, such as acoustic wave pressures in a fluid, in an environment of high static pressures and high temperatures. Ideally, what is needed is such a sensor with a single optical fiber wound about the mandrel at many locations along the length of the mandrel, with one or more of each of the windings sandwiched by a pair of Bragg gratings inscribed in the optical fiber to provide, simultaneously, dynamic pressure measurements for each pair of fiber Bragg gratings. Then for each pair of Bragg gratings that sandwich only a single winding, the dynamic pressure can be measured at the relatively precise location of the winding, and for each pair of Bragg gratings that sandwiches a series of windings, the dynamic pressure averaged over the location of each of the sandwiched windings can be measured.